We consider data living in a non-Euclidean domain described by a possibly directed graph \({\mathcal {G}}=\lbrace {\mathcal {V}}, {\mathcal {E}}, {\mathbf {S}}\rbrace \) , where \({\mathcal {V}}=\lbrace 1, \ldots , N\rbrace \)  is the vertex set, \({\mathcal {E}}\subseteq {\mathcal {V}}\times {\mathcal {V}}\)  is the edge set, and \({\mathbf {S}}\)  is an \(N \times N\)  matrix encoding the topology of the graph. The matrix \({\mathbf {S}}\)  is referred to as the graph shift operator (GSO) and typical instantiations include the (weighted) adjacency matrix \({\mathbf {W}}\)  [1]} and the graph Laplacian \({\mathbf {L}}\)  [2]}. By associating to each node \(i \in {\mathcal {V}}\)  a scalar value \(x(i)\) , we define \({\mathbf {x}}=[x(1), \ldots , x(N)]^\top \in \mathbb {R}^N\)  as a graph signal mapping the node set to the set of real numbers.
